We calculate the optical depth and the number of events due to gravitational microlensing towards the Galactic bulge , the spiral arm directions \gamma Scutum , \beta Scutum , \gamma Normae , \vartheta Muscae and some dwarf galaxies in the halo of the Galaxy .

Using the events found by the MACHO collaboration during their first year of observation towards Baade ’ s Window we estimate the mass functions for the bulge and disk populations following the mass moment method .
We find that the mass function can be described by a decreasing power-law with slope \alpha \simeq 2.0 in both cases and a minimal mass of \sim 0.01 M _ { \odot } for the bulge and \sim 0.02 M _ { \odot } for the disk , respectively .
Assuming that the obtained mass function for the disk is also valid in the spiral arms , we find that the expected number of events towards the spiral arms is in reasonable agreement with the observations .
However , the small number of observed events does not yet constrain much the different parameters entering in the computation of the mass function .

To study the influence of the Magellanic Clouds on the shape and the velocity dispersion in the halo we perform a N-body simulation .
We find that their presence induces a slight flattening of the halo ( q _ { H } \simeq 0.8 ) .
As a result the expected number of microlensing events towards some targets in the halo , such as the LMC or the SMC , decreases by about 20 % , whereas due to the the modification induced on the velocity dispersion the event duration increases .